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Abstract

The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix inequalities for the Dstable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-lime linear systems with polytopic uncertainties.
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Abstract

Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.
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Abstract

Air core solenoids, possibly single layer and with significant spacing between turns, are often used to ensure low stray capacitance, as they are used as part of many sensors and instruments. The problem of the correct estimation of the stray capacitance is relevant both during design and to validate measurement results; the expected value is so low to be influenced by any stray capacitance of the external measurement instrument. A simplified method is proposed that does not perturb the stray capacitance of the solenoid under test; the method is based on resonance with an external capacitor and on the use of a linear regression technique.
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